Here is what I've done a number of times, single handing my Wauquiez Pretorian 35. I sit in Beaufort and wait for winds that will be south of east going south. I wait and wait and wait until that happens. (Beaufort is not such a bad place to wait.) Once I get the desired forecast, I go. Weather forecasts are pretty good for 24-36 hours and you'll be around Hatteras in that time frame. The first 25 miles or so will be reasonably hard on the nose, as to round Cape Lookout you'll be sailing (motoring) south at first. Having rounded Lookout, I pick a spot (waypoint) off Hatteras in about 200 feet of water as my target. Once around Hatteras, I sail north a bit to be comfortably out of the stream and then head off to my destination, be it New York or Newport.
Rounding Hatteras will be a good way to start a 7000 mile voyage. The ICW is something you can save for when you are in your 70s and have a trawler.